Embed Size (px)
Citation preview
PHYSICAL REVIEW B 100, 195302 (2019)
Ab initio treatment of silicon-hydrogen bond rupture at Si/SiO2 interfaces
Markus Jech ,1,* Al-Moatasem El-Sayed,1,2,† Stanislav Tyaginov,1,3,‡ Alexander L. Shluger,4,§ and Tibor Grasser1,‖1Institute for Microelectronics, Technische Universität Wien, A-1040 Vienna, Austria
2Nanolayers Research Computing, Ltd., 1 Granville Court, Granville Road, London N12 0HL, United Kingdom3imec, Kapeldreef 75, B-3001 Leuven, Belgium
4Department of Physics and Astronomy and London Centre for Nanotechnology, University College London,Gower Street, London WC1E 6BT, United Kingdom
(Received 15 March 2019; revised manuscript received 31 July 2019; published 5 November 2019)
Even after more than 50 years of development, a major issue in silicon-based technology is the understandingof the Si/SiO2 interface and its defects, particularly the unsaturated silicon dangling bonds which have to bepassivated by hydrogen during fabrication. Although it is well known that hydrogen dissociation from an initiallypassivated interfacial Si dangling bond results in an electrically active defect, there is still no consensus on theactual microscopic Si–H bond-breaking mechanism, despite a significant research effort. The most thoroughtheoretical study in the field was published by Tuttle and Van de Walle 20 years ago. Although it was thensuggested that the hydrogen dissociates most likely into a bond-center site, no clean argument for bond rupturecould be given at that time. In order to take a fresh look at this highly important problem, we employ thelatest ab initio methods available, including the method of well-tempered metadynamics and nudged-elastic-band calculations based on density functional theory (DFT). This allows us to study the interactions of a Si–Hbond with its realistic environment in a three-dimensional Si/a-SiO2 interface in considerable detail. Usingclassical force fields and well-tempered metadynamics in conjunction with DFT, we provide new insights intothe dissociation kinetics. We find that one of the previously suggested dissociation paths only leads into a neutral,metastable state which would not facilitate bond dissociation. By sampling the configuration space in greaterdetail than ever before, we propose a trajectory whereby the H first moves towards an adjacent Si and in asecond step relaxes into a configuration between the next-nearest Si–Si bond. The final statistical analysis on alarge number of defects on this amorphous interface yields potential energy surfaces and barriers which are inexcellent agreement with experimental values.
DOI: 10.1103/PhysRevB.100.195302
I. INTRODUCTION
Structural disorder and material defects have received asignificant amount of interest due to their diverse implicationsand manifold applications. Particularly in the field of micro-and nanoelectronics, defects are of enormous importancefor semiconductor applications like modern metal-oxide-semiconductor field-effect transistors (MOSFETs). Point de-fects not only determine electrical and optical properties butalso impose limits on the device reliability by creating local-ized trapping sites for electrons and holes. Among the variousdefect configurations observed in modern electronic devices,hydrogen—in one of its many forms—and its interactionwith the surrounding network is of special interest due toits role as a key ingredient in a wide range of technolo-gies. Numerous studies have shown that hydrogen leads tothe formation of defects within amorphous oxides [1–5], inaddition to the pre-existing intrinsic active states associated
*[email protected]†[email protected]‡[email protected]§[email protected]‖[email protected]
with these materials [1,6,7]. On the other hand, hydrogenis well known to passivate electrically active states, whichis essential for producing solar cells [8] and silicon-basedtransistors. Additionally, its ability to relieve strain and itsinfluence on surface reconstruction allows the developmentof emerging technologies beyond complementary metal-oxidesemiconductor (CMOS) applications [9–11].
The deliberate introduction of hydrogen into semiconduc-tor devices during fabrication initially improves their char-acteristics by annealing a particular type of defect at theSi/SiO2 interface known as the Pb center. Using electron-spin-resonance spectroscopy, two electrically active types ofPb defects have been clearly identified on the industrially mostrelevant 〈100〉 surface, called Pb0 and Pb1 [6,12–14]. While thestructural properties of the Pb1 center are still controversial[15–17], the dominant Pb0 center has been identified as atrivalent interfacial Si back bonded to three Si atoms in thebulk [18,19], rendering it consistent with a silicon danglingbond (Si-DB) in the silicon subinterfacial region. However,it was shown that the passivation process can actually bereversed by thermal dissociation [20,21], the interaction withenergetic carriers [22–24], and even during device operation[25–31]. Thus, the dissociation of the Si–H bond plays acrucial role in reliability issues and requires a fundamentalunderstanding of the involved kinetics.
2469-9950/2019/100(19)/195302(11) 195302-1 ©2019 American Physical Society
MARKUS JECH et al. PHYSICAL REVIEW B 100, 195302 (2019)
Experimental data by Brower and Stesmans show a processwith an activation barrier between 2.5 and 2.8 eV [20,21].The pioneering work of Tuttle et al. and Van de Walle et al.used ab initio calculations to investigate the structural andenergetic properties of various configurations of hydrogen inperiodic models of crystalline and amorphous Si [32–39] toexplain Si–H bond rupture. They showed that dissociationvia the stretching mode into free space requires 3.6 eV, theSi–H binding energy, which is too large to be consistent withexperimental data. Instead, they proposed that by interactionswith the surrounding network the dissociation barrier maybe reduced. In agreement with experimental observations[40–42], they suggested that it would be more likely forneutral H to move into a Si–Si bond-center site (referred toas BC site) in bulk Si [43–45]. Being in the BC site, the H isplaced between a strained Si–Si bond and is 1.75 to 2.5 eVhigher in energy than the Si–H configuration, depending onwhether the BC site is adjacent to a Si-DB or anywhere elsein the bulk Si. However, only the different configurations havebeen investigated, and no dissociation pathway connecting theinitial Si–H configuration and the final BC configuration couldbe given at that time. In Ref. [33], the authors speculated thatby bending the H into the antibonding configuration (referredto as AB site), a 180◦ flipped position of the hydrogen,electrically active levels in the Si band gap allow the Si–Hcomplex to become charged and the H to dissociate. However,these results are almost two decades old, and recent progressin DFT development and atomistic simulations allow a moreaccurate description which provides new insights, as we willshow in the following.
While previous work has shown that the AB site is ener-getically higher than the equilibrium site and that the BC sitewould form a suitable configuration for H to diffuse away,this work and the presented results systematically address theremaining open questions: How exactly would the H eventu-ally dissociate away from the Si at the Si/SiO2 environment?To this aim we study how bond breakage occurs by employ-ing various methods, from classical molecular dynamics toab initio calculations, to characterize the Si–H bond at theSi/SiO2 interface. The starting point of our study is a Si/SiO2structure with a silicon dangling bond at the interface whichwas passivated by hydrogen. In order to gain insight into thedefect generation kinetics, we use a combination of state-of-the-art simulation techniques together with a realistic Si/a-SiO2 interface model containing 475 atoms. We applied (well-tempered) metadynamics, an enhanced sampling technique,to simulate the free-energy surface within the vicinity of theinterfacial Si–H bond. In addition to the stable configurationof the intact Si–H bond, two (meta-) stable configurations forthe H atom, including the minimum energy paths connectingthem, could be identified. By employing density functionaltheory calculations, we further investigated the Si–H kinet-ics and also assess the electronic properties for the variousconfigurations to check how additional energy levels in theband gap may aid the dissociation process. These calculationsclearly show that the previously suggested AB site is only ametastable state without energy levels in the Si band gap. Assuch, the AB site is a dead end in the reaction dynamics andwould not facilitate breaking of the Si–H bond. However, ourcalculations clearly suggest a new dissociation pathway for
interfacial Si–H bonds, which is also validated at a statisticallevel. Our results thus provide a more complete understandingof how defects at the Si/SiO2 interface can be created.
II. CALCULATION DETAILS
We use a combination of classical interatomic potentialsand DFT calculations applied on the Si–H bond within thethree-dimensional environment of a Si/SiO2 interface. Here,we give a detailed description of the different methods andtheir applications within this work.
A. DFT setup
All simulations were carried out using the CP2K pack-age [46], a DFT code which uses a mixed Gaussian andplane-waves approach to represent the electrons in the sys-tem. Throughout this work, three-dimensional (3D) periodicboundary conditions were used for the Si/SiO2 system. Adouble-ζ Gaussian basis set optimized for condensed-phasesystems for Si, O, and H was employed in conjunction withthe Goedecker-Teter-Hutter (GTH) pseudopotentials [47,48].The plane-wave cutoff used in these calculations was setto 650 Ry. In order to minimize the errors in the bandgaps and barrier calculations, the nonlocal, hybrid functionalPBE0_TC_LRC was used. This functional contains a 20%contribution of Hartree-Fock exchange and correlation aswell as using a truncated Coulomb operator with a cutoffradius set to 2 Å [49]. To mitigate the computational costof calculating the Hartree-Fock integrals within the nonlocalfunctional, the auxiliary density matrix method (ADMM) wasemployed [50]. In addition to the main basis set, a more sparseauxiliary basis set (pFIT basis set for Si, O, and H) was usedto calculate the Hartree-Fock exchange terms, which allows areduction of computational expenses. The geometry optimiza-tions were performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [51–54] to minimize forces onatoms to within 24 pN (1.5 × 10−2 eV/Å). Energy barriersbetween different atomistic configurations were calculatedusing the climbing-image nudged-elastic-band method (CI-NEB) [55,56]. The algorithm linearly interpolates betweenthe initial and final configuration to generate a trajectory,connected by springs. The whole band is then simultaneouslyrelaxed with the spring’s force constant set to 19.5 eV/Å2.
B. Si/SiO2 interface creation
Constructing credible interface structures between amor-phous oxides and a crystalline substrate has been proven tobe an extremely challenging problem [57–62] due to the lackof detailed information regarding the microscopic interfacialregion. It is known from measurements performed in thin SiO2
films that thermal oxidation of silicon results in an intrinsiccompressive stress within the oxide [63–67]. Depending onthe oxide thickness and the oxidation temperature, the re-ported values are between 0.5 and 2.0 GPa. This stress isalso observed in x-ray reflectivity experiments [68], whichshow an increased density of SiO2 in an Si/SiO2 systemcompared to bulk amorphous silica as well as a compressedSi–O–Si angle distribution [69,70]. Furthermore, transmissionelectron microscope [71,72] (TEM) images and atomic-scale
195302-2
AB INIT IO TREATMENT OF SILICON-HYDROGEN … PHYSICAL REVIEW B 100, 195302 (2019)
electron-energy-loss spectroscopy [73,74] (EELS) indicate atransition region of approximately 5–7 Å between crystallinesilicon and the amorphous structure. Within this interfacialregion the band gap as well as the dielectric constant con-tinuously change between Si and SiO2, as was also foundin recent DFT studies [75,76]. Photoemission measurementswere used to investigate the chemical structure of ultrathininterfaces [71,77]. The data suggest three transition layerswith increasing concentration of partially oxidized siliconacross the interface. All these experimental results provideconstraints a realistic interface model must satisfy.
The methodology used to create a 3D periodic Si/SiO2interface model with two interface regions adapts the melt andquench procedure previously used to create a-SiO2 cells [1,3].Due to the excessive calculation steps required for reliablemodels within molecular dynamics (MD) simulations, theReaxFF force field [78] implemented in the LAMMPS code[79] was used. Starting from a 3 × 3 × 3 β-cristobalite cell,whose lateral cell dimensions were fixed to that of silicon,we minimized the energy by allowing the cell to move inthe c direction. It was found that this procedure gives adensity of ∼2.3 g/cm3, in agreement with measured values[71]. Subsequently, the cell dimensions were fixed during themelt and quench procedure. The first layer of Si atoms oneither side was frozen while the remaining atoms were givenrandom velocities from a Gaussian distribution. First, thesystem was equilibrated at 300 K for 10 ps using a Berendsenthermostat. Afterwards the temperature was linearly increasedto 5000 K over 60 ps to melt SiO2 and further equilibratedfor an additional 100 ps, followed by a quench to 0 K at arate of 1.6 K/ps. In the final step crystalline Si was addedat the top and bottom of the model, undercoordinated atomswere passivated by hydrogen, and the structure was allowed torelax at 300 K. In total over 100 Si/SiO2 models were created,which resulted in various defect configurations at the interfaceas well as in the oxide. The three most promising models,in terms of their geometrical properties such as coordinationnumber, were chosen for this study and further examined aswell as optimized using our DFT setup. Simulations of thenonoptimized interface indeed gave rise to an intrinsic stressof 3.5 GPa, as mentioned above. Thus, in order to obtain amore realistic interface model for our subsequent DFT simula-tions, we applied an external pressure of 1 GPa parallel to theinterface and performed a full cell optimization including theionic positions of the model where the initial tetragonal cellsymmetry was kept fixed. All three structures converged toalmost the same cell size, a = b = 16.203 Å, c = 32.965 Å,with a variance of 0.007 Å in the lateral dimensions and0.014 Å in the c direction.
The extracted geometrical properties of the final interfacemodels are in good agreement with experimental data. TheSi–O bond length ranges from 1.46 to 1.84 Å(ReaxFF: 1.52–2.04 Å) and peaks at around 1.64 Å(ReaxFF: 1.61 Å), whichis consistent with infrared absorption measurements [71]. TheSi–O–Si angle averages at 133.5◦ (ReaxFF: 121.4◦), whichagrees well with the conclusions reached in Ref. [70], that theangle is reduced to 135◦ compared to 148◦ in bulk structures,while the O–Si–O angles remain almost unchanged comparedto bulk SiO2 (∼109◦, ReaxFF: ∼109◦). To further quantify thequality of the interface, we calculated the deformation of the
1 2 3 4 51 2 3 4 5
−6
−3
0
3
6
Ener
gy[e
V]
1 2
DOS [arb. units]
3
EC
EV
4 5
0.0
0.5
1.0
1.5
Cha
rges
[e]
0.0
0.1
0.2
0.3
0.4
0.5
Dis
plac
emen
t|Δx|
[A]
FIG. 1. A density functional theory simulation of the chosenSi/a-SiO2/Si interface structure containing 475 atoms. The upperpanel shows the charges calculated with Mulliken population anal-ysis across the interface model. One can see a gradual change fromelemental silicon to fully oxidized silicon with the first 2–3 transitionlayers. The middle panel shows the interface model and the displace-ment of the Si atoms from their respective equilibrium position inc-Si. Blue (dark atoms in region 1 and 5) means a displacementof less than 0.2 Å, while the highlighted red atoms (dark atoms inregion 2 and 4) at the interface are strongly displaced. The bottompanel shows the density of states at different positions across theslab. Our results are in good agreement with well-established results.The band gap of Si as well as of a-SiO2 is underestimated byabout ∼10% (compared to Eg,Si = 1.12 eV and Eg,SiO2 = 9.1 eV).For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.
c-Si lattice as the deviation of the atomic positions from theirrespective positions in crystalline silicon, see Fig. 1 (middlepanel). One can clearly see that already three layers awayfrom the Si/SiO2 interface the crystal structure is almost com-pletely restored, with displacements less than 0.2 Å. However,directly at the transition layer, distortions are stronger due tothe formation of Si–O bonds, giving rise to a higher strain atthe direct interface between Si and SiO2. In addition to thestructural quality we also analyzed the electronic structureof the interface system. Figure 1 (upper panel) shows theoxidation state of silicon atoms across the Si/SiO2 modelusing Mulliken population analysis. The profile clearly showsa gradual change from Si0 in the crystalline Si part to its fullyoxidized form Si+4 (which corresponds to a net charge of∼1.4e in our DFT setup) in the SiO2 region over a ∼5-Å tran-sition region, which is qualitatively very similar to the results
195302-3
MARKUS JECH et al. PHYSICAL REVIEW B 100, 195302 (2019)
(a) (b) (c)
FIG. 2. Three examples of silicon dangling bond interface de-fects created within the Si/SiO2 interface models. Configuration(a) at a first glance is consistent with a Pb1 center (back bonded to twoSi and one O atom). The spin density suggests that the defect stateis mainly a nonbinding p orbital, which contradicts experimentalresults [12,13,18] and therefore was not further considered. Config-urations like (b) have an extra H next to the passivated defect whichmight distort the calculation results and were also not considered.Finally, configuration (c), where the unpassivated Si is trivalentlybonded to three other Si’s, with an sp3 hybridized dangling bondorbital, appeared closest to the well-known Pb0 center and was usedin this study.
of Ref. [77]. This is also reflected in the calculated densityof states (DOS) across the model, see Fig. 1 (lower panels).While in the bulk regions (1, 3, and 5) the corresponding bandgaps (0.95 and 8.58 eV) compare well to the known values(1.1 eV for Si and 8.9 eV for a-SiO2), one can see a continuouschange of the band gap within the interfacial regions (2 and 4).Furthermore, one can see additional electronic states withinthe band gap for the interface (2 and 4) and the bulk SiO2 (3)regions. These induced states can be identified as silicon-bandwave functions extending into the near oxide region. Suchfeatures have also been reported in recent experimental studies[73,74], where the authors conclude that this limits the prac-tical oxide thickness to 1.2 nm. It may be inferred that withinour interface model, having an oxide thickness of 1.1 nm, evenregion 3 does not exhibit actual full bulk SiO2 properties.
The preselected (using ReaxFF) and optimized (usingDFT) interface models possess three different silicon danglingbond configurations (which were passivated by H) at the in-terface; see examples in Fig. 2. From electron-spin-resonancestudies the characteristics of Si/SiO2 interface defects, knownto be Pb centers, are well known: A trivalent interfacial Si,back bonded to three Si atoms in the bulk with an sp3
hybridized dangling bond orbital. As can be seen in Fig. 2,configurations like those in (c) fully meet these requirementsand were therefore chosen for our study. Further structuraldetails including the atomistic models as well as a defectanalysis can be found in the Supplemental Material [80].
To summarize, we created different Si/SiO2 interfacestructures by adapting the melt and quench procedure. Whilethe equilibrated models using the ReaxFF force field areused as a starting point for our metadynamics simulations,further geometry and cell optimizations within our DFT setupprovide fully relaxed models for the ab initio calculations,see Sec. III. Both methods give qualitatively similar resultsand properly reflect experimental observations such as anabrupt transition region, geometrical statistics, and the siliconoxidation state profile across the interface. Optimization using
DFT even improved the geometrical analysis and also showeda good agreement of the calculated electronic structure withexperiments. A recent study [81] investigated the applicabilityof ReaxFF to model glassy silica. The authors concluded thatReaxFF has a promising potential for creating and modelingamorphous systems and would even allow study of the surfacereactivity, thanks to its ability to dynamically form and breakbonds.
III. RESULTS
In order to establish the detailed kinetics responsible forthe creation of silicon dangling bonds, we investigate theSi–H bond properties in a realistic Si/SiO2 interface model.We employ well-tempered metadynamics using a classicalforce field to explore the potential landscape in the vicinityof the interfacial Si–H bond. Building on these results, wethen investigate the Si–H dynamics more accurately by usingDFT, which enables us to identify the most likely dissociationpathway for creating an interface defect.
A. Metadynamics
Well-tempered metadynamics allows one to sample thefree-energy landscape in the direct vicinity of the Si–H bondby driving the system out of its equilibrium. Thus, thismethod is well suited for finding (meta-) stable configurationsand dissociation pathways for the hydrogen at the interface.However, the large amount of simulation steps necessary toconverge such a simulation, together with the rather largeSi/SiO2 model system, permits the use only of a classicalforce-field. We used the ReaxFF force field [78] implementedin LAMMPS [79] in combination with PLUMED [82]. As thestarting point for these calculations we chose an equilibrationphase for 100 ps at T = 300 K by assigning random, normallydistributed velocities to the whole system. Subsequently, weran well-tempered metadynamics simulations for differentsimulation times and bias factors to make sure that the re-sults are converged. Within these simulations we defined twocollective variables (CVs) which were biased and monitoredduring the calculations: the Si–H bond distance r as well asthe polar angle φ with respect to its equilibrium configura-tion. The azimuthal angle, however, was only monitored andnot explicitly biased within the metadynamics simulations.Furthermore, we restricted the bond distance to within 4 Å,which ensured sampling of the free-energy landscape only inthe direct vicinity of the Si–H bond. Additional computationaldetails are given in the Appendix.
The resulting free-energy landscape is shown in Fig. 3. Arepresentation in 3D space is given in the upper panels ofFig. 3, which shows the isosurface for three values of thepotential energy. In order to give a more intuitive picture of thefree energy, we mapped the potential onto 2D space by onlyconsidering the CV r and the polar angle φ, see Fig. 3. Threedistinct minima can be identified: (1) corresponds to the intactSi–H bond in its equilibrium configuration, (3) represents theH in the AB site, and (5) marks the newly identified minimumformed by the H being in the next but one BC site between Si2
and Si3.The respective atomistic configurations are schematically
illustrated in the right panel of Fig. 3. In addition, to extract
195302-4
AB INIT IO TREATMENT OF SILICON-HYDROGEN … PHYSICAL REVIEW B 100, 195302 (2019)
1.0 1.5 2.0 2.5 3.0 3.5 4.0Distance r [A]
-90
0
90
180
Ang
leφ
[deg
]
1
3
2 45
1 intact Si–H
2 H @ BC1,2
3 H @ AB
4 H @ Si2
5 H @ BC2,3
0.3
0.8
1.2
1.2
1.8
1.8
1.82.2
2.2
2.4
2.4
Si1
Si2
Si3
1
35
4
2
E=0.8 eV E=1.8 eV E=2.4 eV
FIG. 3. The free-energy landscape (in a 3D and 2D representation) together with a schematic of the atomistic structure in the vicinity ofthe interfacial Si–H bond obtained from the ReaxFF force field. Three distinct minima are visible: The equilibrium position (1) at r = 1.37 Åand φ = 0◦, the H in the AB site labeled with (3), as well as the BC2,3 configuration (5) where the H moved in between the Si2–Si3 bond. Thecrosses (2) and (4) mark the transition barriers for the minimum energy paths (lines) connecting the different minima.
the minimum energy paths (MEPs) connecting the differentminimum configurations, we used more efficient CVs, suchas r′ = 1/
√2(rSi3,H − rSi1,H) or simply the angle φ.
Inverting the H around Si1 into the AB site (3), whichis 0.8 eV higher in energy, proceeds via the dashed path inFig. 3. The energy of the transition state is 1.75 eV, and itsconfiguration corresponds to the H being in the BC1,2 site (2).It is interesting to note that although the H forms a bond-centerconfiguration between the Si1–Si2 bond, this is not a preferredand stable configuration for the H atom along the given path,contrary to the fact that in crystalline bulk Si the BC site is astable configuration of H.
In addition, the hydrogen can be moved into the BC2,3
configuration (5), shown as the solid black line in Fig. 3.The extracted MEP yields a transition state (4) where theH is stretched away from its initial Si (Si1) and attached tothe adjacent Si (Si2). With a forward barrier of 2.25 eV anda backward barrier of 1.05 eV, this trajectory is a promis-ing candidate to explain the measurement data in Ref. [83],which reports barrier heights of 2.83 and 1.51 eV for theforward and reverse process, respectively. The dotted linein Fig. 3 shows the MEP connecting the AB site (3) andthe BC2,3 configuration (5). No additional transition couldbe found, and thus the reaction would again proceed overstate (4), making the AB site a dead end in the reactiondynamics.
B. DFT
To further investigate the Si–H kinetics and assess theelectronic structure for the various configurations we employDFT simulations. Building on the results of the metadynam-ics simulations, we ran CI-NEB calculations to identify thebond-breaking dynamics. The initial and final configurationsobtained from the classical force-field calculations were usedto construct a trajectory with 13 frames in total by usinglinear interpolation (note that this corresponds to a directconnection between the minima in Fig. 3). Subsequently, CI-NEB simulations optimized the band, including its endpoints.
1. Trajectory 1: Si–H → BC2,3
First, we analyzed the direct path between the equilibriumSi–H configuration (1) and the BC2,3 site (5) in more detail,as it appears most promising in terms of capturing the reac-tion dynamics. Figure 4 shows the resulting energy barrieralong the calculated path together with the respective atomicstructures and the projected DOS onto Si1. The calculatedtrajectory possesses very similar features, as already observedin Fig. 3. The hydrogen first moves towards Si2, marking thereaction barrier, and eventually moves in between the Si2–Si3 bond which was stretched from 2.34 to 3.13 Å, therebyforming a BC configuration. The total energy barrier along thedirect trajectory which separates the intact Si–H configuration
195302-5
MARKUS JECH et al. PHYSICAL REVIEW B 100, 195302 (2019)
0.0 0.2 0.4 0.6 0.8 1.0Reaction Coordinate [arb. units]
0
1
2
3
Ener
gy[e
V]
1
45
DFTMD
Si1
Si2
Si3
1)
Si1
Si2
Si3
4)Si1
Si2
Si3
5)
-1 -0.5 0 0.5 1.0 1.5Energy, E− EF [eV]
0.0
0.1
0.2
0.3
ΔD
OS
[arb
. uni
ts]
EV EC
1 intact Si–H 4 H@Si2 5 H@BC2,3
HOMO-1 LUMO+1 HOMO LUMO Spin density
FIG. 4. A climbing image nudged-elastic-band (CI-NEB) simulation investigating the direct MEP connecting the intact Si–H configuration(1) and the next-nearest BC site between Si2 and Si3 (5) via the transition state (4) where the H is attached to the adjacent Si2. The total energyrequired for the forward reaction is 2.77 and 1.30 eV for moving the H back to its initial configuration. The right panel shows the differenceof the projected DOS onto the Si1 atom compared to the intact Si-H configuration. It is clearly visible that the transition state and also thefinal state introduce localized electronic states in the Si band gap. Additionally, the lower panels show the resulting wave functions of the finalstate (5). The HOMO-1 and the LUMO + 1 orbital are delocalized Si band states (which, however, penetrate into the oxide region), whereasthe HOMO and LUMO orbitals are localized around the Si-DB. The spin density suggests the dangling bond to be constituted by a slightlydistorted unpaired Si sp3 hybrid orbital.
and the BC2,3 site is 2.77 eV for the forward reaction and1.30 eV for repassivating the Si dangling bond. Comparedto the classical force-field calculation, both values are evencloser to the experimentally extracted barriers for breaking(2.83 eV) and passivating (1.51 eV) an interfacial Si–H bond.Furthermore, the transition state (4) and the final state (5) in-troduce a localized electronic level in the Si band gap, a filledstate close to the valence band edge, as well as an empty levelin the upper half of the band gap, seen in Fig. 4. A detailedanalysis can be given in terms of the molecular orbitals (MO)associated with these two states and the spin density. Bothintroduced band-gap states, which are the highest (lowest)occupied (unoccupied) MOs of the interface structure, arefully localized around the unpassivated Si, in contrast to thenext lower (higher) band state. Furthermore, the spin densityis not only localized around the central Si atom but alsoexhibits a significant spread onto the back-bonded Si atoms.Overall this suggests a (slightly distorted) sp3-hybridized Sidangling bond.
To better understand the individual bonding configurationsalong the trajectory, we also analyzed the charges associatedwith the involved Si and H atoms by using Mulliken popula-tion analysis as well as the method of Bader charge analysis.Both methods yield the same result: The H indeed dissociatesin its neutral charge state with one remaining electron on thecreated Si-DB. All details are given in the Appendix.
2. Trajectory 2: Si–H → AB → BC2,3
Additionally, we investigate trajectory 2, which involvesthe hydrogen invert into the AB position (3) and subsequentlymoves into the bond-center site formed between Si2 and Si3
(5). The CI-NEB results are shown in Fig. 5 together with thecorresponding atomistic configurations. In an initial step the Hbends into the BC1,2 site which marks the first transition statein Fig. 5 with a reaction barrier of 2.2 eV. Thereby the Si1–Si2
distance increased by 0.64 Å to form the BC configuration.Subsequently, the H relaxes into the metastable AB site.
195302-6
AB INIT IO TREATMENT OF SILICON-HYDROGEN … PHYSICAL REVIEW B 100, 195302 (2019)
0.0 0.2 0.4 0.6 0.8 1.0Reaction Coordinate [arb. units]
0
1
2
3
Ener
gy[e
V]
1
2
3
4 5
DFTMD
Si1
Si2
Si3
1)
Si1
Si2
Si3
2)
Si1Si2
Si3
3)
Si1Si2
Si3
4 )
Si1Si2
Si3
5)
-1 -0.5 0 0.5 1.0 1.5Energy, E− EF [eV]
0.0
0.1
0.2
0.3
ΔD
OS
[arb
. uni
ts]
EV EC
1 Si–H 2 H@BC1,2 3 H@AB 4 H@Si2 5 H@BC2,3
FIG. 5. The results of CI-NEB simulations bending the hydrogen from its equilibrium position (1) through the plane of an adjacent Si1–Si2
bond (2) into an inverted AB configuration (3). The energy barrier to overcome is 2.2 eV without any additional minimum along the path. Mostimportantly, one can see that no electronic states appear in the band gap at any position along the path from (1) to (3), indicating that the Si–Hbond remains intact. Moving the H from the AB site (3) into the BC2,3 configuration (5) proceeds over the transition state (4′) where the H isattached to Si2 with a reaction barrier of 2.25 eV. This additional path indeed creates defect levels in the band gap of silicon, see Fig. 4.
Such a trajectory was also investigated by Tuttle and Van deWalle with a similar energy profile [33,39] and suggested toprovide a possible pathway for H desorption. In particular,they suggested that the H in the AB configuration leads toenergy levels in the Si band gap, which, upon charge capture,would lead to the breaking of the Si–H bond. However, ascan be seen in the bottom right panel in Fig. 5, which showsthe change in the projected density of states (pDOS) onto Si1
compared to the equilibrium Si–H configuration, no additionalstates in the Si band gap are formed for positions (2) and (3).Thus, the results suggest that such a transition does not allowthe Si–H complex to become charged and/or dissociate.
Therefore, we further investigated the trajectory connect-ing state (3) and (5), the bond-center configuration betweenSi2 and Si3, which is shown as the dotted line in Fig. 3.Figure 5 shows the corresponding energy with a reactionbarrier of 2.25 eV relative to (3) formed by the transition state(4′), where the hydrogen is attached to Si2. This path indeedcreates localized electronic states in the band gap of silicon,as can be seen in the analysis of the DOS and is alreadymentioned above.
Quite reassuringly, the qualitative behavior of both results,the DFT as well as the MD simulations (shown in Fig. 3), israther similar and predicts the same kinetics for the hydrogen.This can be seen best when the H moves from (3) towardsstate (4′). Even the ab initio simulations show that the lat-tice relaxation—particularly pronounced for Si1—necessaryto reach the AB site must be partially reversed to move theH towards Si2. However, note that although the classical MD
simulations predict a unique transition state (4) (Fig. 3) forboth paths, (1)→(5) and (3)→(5), the CI-NEB simulationsfound two distinct configurations. While in both transitionstates the H is attached to Si2 with a distance of 1.65 Å (4)and 1.68 Å (4′), respectively, the position of H with respect toSi2 differs, as can be seen in Figs. 5 and 4.
Summarizing our results suggests the following: To breaka Si–H bond at the Si/SiO2 interface and create an electricallyactive Si dangling bond, the hydrogen needs to move intoa stable BC site between the next but one Si–Si bond, e.g.,Si2 and Si3. We propose the direct path connecting state (1)and (5) to be the preferred dissociation trajectory due to theslightly reduced reaction barrier and the lattice relaxationsinvolved compared to the pathway including the AB site asan intermediate state.
IV. STATISTICAL ANALYSIS
Structural disorder at the Si/SiO2 interface results in adistribution of Si–Si (and Si–O) bond lengths and angles.Thus, linking theoretical data and experimental results re-quires a statistical comparison. For our analysis we usedthree different Si/a-SiO2 models, see Sec. II, and in total13 variations of pristine Si–H bonds which were consistentwith Pb center configurations. The Si–H configurations werecreated by breaking and passivating selected Si–Si or Si–Obonds and thus, also include Pb1-like types [see Fig. 2(a)] andconfigurations with nearby H atoms [see Fig. 2(b)]. In order tofacilitate comparison with experimental results, which suggest
195302-7
MARKUS JECH et al. PHYSICAL REVIEW B 100, 195302 (2019)
2.0 2.5 3.0Energy [eV]
0
2
4
6
8
10
Dis
trib
utio
n[1
]
EB,forward
μ = 2.57 (2.64) eVσ = 0.20 (0.11) eV
1.0 1.5 2.0Energy [eV]
EB,backward
μ = 1.31 (1.30) eVσ = 0.23 (0.13) eV
FIG. 6. Distribution of calculated barriers using the CI-NEBmethod. The statistics includes 38 simulated dissociation paths forvarious initial Si–H configurations, see Fig. 2. While the colored barsshow the full result, the gray bars present a limited statistics, wherethe initial configuration is at least one layer away from the interfaceand properly reflects the characteristics of Fig. 2(c).
that the dominant defect at the (100)Si/SiO2 interface is aSi-DB back bonded to three other Si atoms, all initial Si–Hbonds are placed within 4 Å of the subinterfacial Si side. Thethree next-nearest BC2,3 sites were chosen, and the directtrajectory was calculated using the CI-NEB method. Overall,38 dissociation paths have been calculated and analyzed, seeFig. 6. We note that owing to computational limitations theCI-NEB simulations have been performed using the PBEfunctional. Subsequently, single point calculations based onthe hybrid PBE0 functional were carried out on the optimizedstructures along the trajectory. The final results are shown inFig. 6.
The calculated defect creation trajectories show a broaddistribution of barriers to break or repassivate the Si–H bond,ranging from 2.07 (0.95) to 2.95 eV (1.94 eV) with a standarddeviation of 0.20 and 0.23 eV, respectively. Mean values forboth barriers are in good agreement with recent experimentalstudies, averaging at 2.57 eV (exp. 2.83 eV) for the forwardreaction and 1.31 eV (exp. 1.51 eV) for the backward barrier.However, the calculated standard deviations σ are actuallylarger than extracted by measurements (exp. σB,f = 0.08 eV,σB,b = 0.06 eV). One possible reason for the wide distributionof barriers is the spatial position of the Si–H bond. Ourstatistics also includes Si–H bonds directly at the Si/SiO2
interface, where Si atoms experience the maximum distortiondue to the amorphous oxide, see Fig. 1. Limiting the statisticsto the initial Si–H configuration residing in an interfacial Sienvironment, which means at least one layer away from theSi/SiO2 transition, results in a much narrower distributionof barriers, see Fig. 6 (gray bars). The concept that interfacedefects are more likely to be in the subinterfacial Si region wasalready mentioned in recent publications [19,84] and furthervalidates this assumption.
From these statistical observations we conclude that theproposed dissociation pathway, where the hydrogen atomsmove from an initial Si–H configuration into a bond-center site between the next-nearest Si-Si bond, is a good
candidate to explain the defect creation process at Si/SiO2
interfaces.
V. DISCUSSIONS AND CONCLUSIONS
We have investigated the pathways and barriers for dissoci-ation of the Si–H bond at the Si/SiO2 interface and examineddifferent dissociation pathways to create a Si dangling bonddefect. Due to its significant technological importance, theliterature already offers a wealth of information. Experimentaldata correlated with the creation of a silicon dangling bondat the Si/SiO2 interface by dissociating hydrogen show areaction barrier of 2.83 ± 0.08 eV [21,83]. Despite extensivetheoretical work by Tuttle et al. and Van de Walle et al., whoinvestigated hydrogen-related configurations in crystallineand amorphous silicon models [32–39], there is still no clearpicture regarding the actual Si–H dissociation kinetics.
To explore the potential energy surface in the vicinity of theSi–H bond and identify possible dissociation pathways, wehave applied well-tempered metadynamics. This method al-lows one to perform enhanced sampling in molecular dynam-ics simulations, aside from equilibrium configurations. Usinga classical force field within these simulations, three distinctminimum configurations for the hydrogen could be found:the intact Si–H in its equilibrium configuration, the invertedbond known as the antibonding site (AB site), as well as abond-center configuration (BC site) where a Si–H–Si complexis formed between the next-nearest Si–Si bond. The resultingminimum energy paths connecting the different minimumconfigurations were further investigated and confirmed byCI-NEB DFT simulations. Quite surprisingly, the qualitativebehavior of the MEPs for both approaches is rather similar.Our analysis shows that the trajectory for bending the H intothe AB site does not allow the Si–H bond to break, contraryto what was suggested by Tuttle et al. [33,34]. Flipping theH into the AB site increases the Si–H bond length from 1.46to 1.51 Å while the Si–Si distances remained constant. Theassociated electronic state indeed shifted by ∼0.2 eV closerto the Si valence and conduction band edges; however, nostate within the band gap appeared. Test calculation in bulk Sishowed the same result, which further validates the presentedresults. However, we propose a dissociation pathway wherethe H moves along the direct MEP into the next but one BCsite to be responsible for the creation of active defects at theSi/SiO2 interface. Our data clearly show that the H dissociatesin its neutral charge state and indeed creates a Si danglingbond with two states in the Si band gap, a filled state in thelower half, as well as an empty state in the upper half of theband gap. The final result yields a forward barrier of 2.77 eVand a barrier of 1.30 eV for the passivation of the Si danglingbond with the H. Both values are in very good agreement withexperimental results published by Stesmans [83].
Additionally, due to the amorphous nature of SiO2 andstructural disorder at the Si/SiO2 interface we performed astatistical analysis. We used three different interface modelsand 13 variations of pristine Si–H bond configurations placedwithin 4 Å of the subinterfacial Si side. CI-NEB calculationshave been performed for the direct trajectory to the threenext-nearest BC2,3 sites, resulting in a total number of 38dissociation pathways. The calculated mean values for the
195302-8
AB INIT IO TREATMENT OF SILICON-HYDROGEN … PHYSICAL REVIEW B 100, 195302 (2019)
forward and backward barrier average at 2.57 eV ± 0.20 eVand 1.31 eV ± 0.23 eV, respectively, which is in good agree-ment with experimental data (2.83 and 1.51 eV). Limitingthe statistics to initial configurations within the subinterfacialSi region, as was mentioned in recent publications, resultsin a narrower distribution of barriers and further improvesthe agreement with experimental data, with EB,forward =2.64 eV ± 0.11 eV and EB,backward = 1.30 eV ± 0.13 eV.
ACKNOWLEDGMENTS
The work was supported in part by the Austrian ScienceFund (FWF) under Project No. P 26382-N30, in part bythe Austrian Research Promotion Agency (FFG, Take-OffProgram) under Project No. 861022, and in part by theEuropean Union’s Horizon 2020 Research and InnovationProgramme under Marie Sklodowska-Curie Grant Agree-ment No. 794950. A.L.S. acknowledges funds provided bythe UK Engineering and Physical Sciences Research Coun-cil (EPSRC) under Grants No. EP/K01739X/1 and No.EP/P013503/1 and by the Leverhulme Trust RPG-2016-135.Furthermore, the authors acknowledge support from the Vi-enna Scientific Cluster for providing resources on the Austrianhigh-performance cluster VSC3.
APPENDIX
A. Metadynamics simulations
In total 30 well-tempered metadynamics simulations withbias factors between 80 and 180 as well as bias heights rang-ing from 9 to 20 meV were conducted. The accessible regionduring the simulations was limited, as can be seen in the upperpanel of Fig. 7. It should be noted that simulations with largebias factors and/or heights did not converge properly, and noreasonable free-energy surface could be extracted. However,simulations with smaller values (bias factors 80/90, biasheights 9–10 meV) indeed converged to the unique potentiallandscape shown in Fig. 3. The simulation result used inSec. III was obtained by performing 50 × 106 time steps witha step size of 0.5 fs. In total, the added bias consisted of1 × 105 Gaussian functions, each with a width of 0.5 Å and aheight of 9 meV, which was used to calculate the free-energysurface. The bottom panel of Fig. 7 assesses the convergenceof the simulation by showing the minimum energy path asa function of the simulation time. It can be clearly seenthat the reconstructed paths for the 20- and 25-ns simulationtime are almost on top of each other, thereby indicating theconvergence of the simulation.
B. Charge analysis
The complex dissociation pathway proposed in Sec. III,which involves the interaction of the bending and stretchingmode of the Si–H bond, requires a detailed understanding ofthe charge states of the corresponding atoms. Thus, we appliedMulliken population analysis as well as Bader charge [85–88]analysis to quantify the total electronic charge associated withthe atoms. Both methods show that the hydrogen would actu-ally dissociate in its neutral charge state, with one remainingelectron on the Si dangling bond. This is clearly visible in
0.0 0.2 0.4 0.6 0.8 1.0Reaction Coordinate [arb. units]
0.0
0.5
1.0
1.5
2.0
2.5
Ener
gy[e
V]
1
4
5
1 ns5 ns10 ns
15 ns20 ns25 ns
FIG. 7. Details of the well-tempered metadynamics simulations.The accessible spatial region during the simulation is shown asthe blue sphere in the upper panel. It includes the subinterfacialregions on either side of the Si/SiO2 interface. The lower panelassesses the convergence of the final simulation results. While fora 1-ns simulation time only the direct vicinity of the equilibriumconfiguration is explored, the minimum energy path connecting 1and 5 barely changes between 20 and 25 ns, which indicates theconvergence of the simulation run.
Fig. 4, a filled state associated with the dangling bond in thelower half of the band gap and an empty state in the upper half.
charge densitydifference
ρ(r) − ρ0(r)
charge density
ρ(r)
Si1 Si2
Si3
FIG. 8. The charge density is represented by the blue and redtranslucent profiles along the dissociation path (blue: increase ofcharge density, red: decrease of charge density). In the initial step theH attaches to an adjacent Si atom (Si2) with a distance of 1.57 Å.Thereby, one electron remains on the initial Si1 as indicated bythe Bader charge analysis. In the final configuration the H forms aSi–H–Si complex between the next-nearest Si2–Si3 bond, as shownin the right panels. Being in this position, the H is slightly negativelycharged and nearly fully bonded to Si3 suggested by the chargedensity as well as the distances to Si2 and Si3.
195302-9
MARKUS JECH et al. PHYSICAL REVIEW B 100, 195302 (2019)
Details of the Bader charge analysis are given in Fig. 8. Theevolution (lower panels) as well as the change (upper panels)of the electronic density are shown at selected points along thedissociation pathway. One can clearly see that the H movesfrom the initial Si1 to an intermediate configuration at the topof the transition barrier, where it is bound to the neighboringSi2 and subsequently into its final BC position between Si2
and Si3. Integration of the associated Bader volumes of Si1
shows that the charge associated with it changes by 0.78e asthe H migrates to Si2, and by 0.95e for the H being in its finalposition. This indicates that one electron remains on the Sidangling bond created during this process. Analyzing the Halong the trajectory shows that its charge changes by 0.18e,becoming slightly negatively charged in its final position.However, from this we conclude that the H would dissociatein its neutral charge state. Another important detail we wantto note is the final position of the hydrogen atom. Along the
trajectory the H first attaches to Si2 until it moves to its finalposition between Si2 and Si3, which is already mentioned inthe literature [38,40,89–91] to be a stable position for H0.However, a closer look reveals that the H would actually bebound to Si3, as suggested by the electronic density, see Fig. 8.This is also reflected by the distances between the H andthe respective Si atoms. While at the transition point the His 1.65 Å from the Si2, this distance increases to 1.68 Å forthe final position, compared to 1.55 Å between the H and Si3.Thus, Si2 also possesses the character of a Si dangling bondwith one unpaired electron. However, no additional states inthe Si band gap are created, which we assume is due to theinteraction with the nearby H atom moving its energy levelbelow the valence band. Within this context, it would be ofinterest to further investigate the effect of external chargesonto the final Si–H–Si complex, as already mentioned in theDiscussion.
[1] Y. Wimmer, A.-M. El-Sayed, W. Gös, T. Grasser, and A. L.Shluger, Proc. R. Soc. London, Sec. A 472, 20160009 (2016).
[2] A.-M. El-Sayed, M. B. Watkins, T. Grasser, V. V. Afanas’ev,and A. L. Shluger, Phys. Rev. Lett. 114, 115503 (2015).
[3] A.-M. El-Sayed, Y. Wimmer, W. Goes, T. Grasser, V. V.Afanas’ev, and A. L. Shluger, Phys. Rev. B 92, 014107 (2015).
[4] A.-M. El-Sayed, M. B. Watkins, T. Grasser, V. V. Afanas’ev,and A. L. Shluger, Microelectron. Eng. 147, 141 (2015).
[5] M. Kaviani, V. V. Afanas’ev, and A. L. Shluger, Phys. Rev. B95, 075117 (2017).
[6] P. Lenahan, Microelectron. Eng. 69, 173 (2003).[7] F. Cerbu, O. Madia, D. V. Andreev, S. Fadida, M. Eizenberg, L.
Breuil, J. G. Lisoni, J. A. Kittl, J. Strand, A. L. Shluger, V. V.Afanas’ev, M. Houssa, and A. Stesmans, Appl. Phys. Lett. 108,222901 (2016).
[8] M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C.Ballif, Renewable Sustainable Energy Rev. 76, 1497 (2017).
[9] S. R. Schofield, P. Studer, C. F. Hirjibehedin, N. J. Curson, G.Aeppli, and D. R. Bowler, Nat. Commun. 4, 1649 (2013).
[10] B. Naydenov and J. J. Boland, Nanotechnology 24, 275202(2013).
[11] L. Gao, P. P. Pal, T. Seideman, N. P. Guisinger, and J. R. Guest,J. Phys. Chem. Lett. 7, 486 (2016).
[12] A. Stesmans and V. V. Afanas’ev, Appl. Phys. Lett. 82, 4074(2003).
[13] A. Stesmans and V. V. Afanas’ev, Phys. Rev. B 57, 10030(1998).
[14] K. Keunen, A. Stesmans, and V. V. Afanas’ev, Phys. Rev. B 84,085329 (2011).
[15] K. Kato, T. Yamasaki, and T. Uda, Phys. Rev. B 73, 073302(2006).
[16] E. H. Poindexter, P. J. Caplan, B. E. Deal, and R. R. Razouk,J. Appl. Phys. 52, 879 (1981).
[17] A. Stesmans and V. V. Afanas’ev, J. Phys.: Condens. Matter 10,L19 (1998).
[18] P. M. Lenahan and J. F. Conley, J. Vac. Sci. Technol., B:Microelectron. Nanometer Struct.–Process., Meas., Phenom.16, 2134 (1998).
[19] A. Stesmans, B. Nouwen, and V. Afanas’ev, Phys. Rev. B 58,15801 (1998).
[20] A. Stesmans, J. Appl. Phys. 88, 489 (2000).[21] K. L. Brower, Phys. Rev. B 42, 3444 (1990).[22] J. W. Lyding, K. Hess, and I. C. Kizilyalli, Appl. Phys. Lett. 68,
2526 (1996).[23] P. Avouris, R. Walkup, A. Rossi, H. Akpati, P. Nordlander, T.-C.
Shen, G. Abeln, and J. Lyding, Surf. Sci. 363, 368 (1996).[24] P. Avouris, R. Walkup, A. Rossi, T.-C. Shen, G. Abeln, J.
Tucker, and J. Lyding, Chem. Phys. Lett. 257, 148 (1996).[25] M. Bina, S. Tyaginov, J. Franco, K. Rupp, Y. Wimmer, D.
Osintsev, B. Kaczer, and T. Grasser, IEEE Trans. ElectronDevices 61, 3103 (2014).
[26] S. Tyaginov, M. Jech, J. Franco, P. Sharma, B. Kaczer, and T.Grasser, IEEE Electron Device Lett. 37, 84 (2016).
[27] C. Guerin, V. Huard, and A. Bravaix, J. Appl. Phys. 105, 114513(2009).
[28] A. Bravaix, Y. M. Randriamihaja, V. Huard, D. Angot, X.Federspiel, W. Arfaoui, P. Mora, F. Cacho, M. Saliva, C. Besset,S. Renard, D. Roy, and E. Vincent, in 2013 IEEE InternationalReliability Physics Symposium (IRPS) (IEEE, New York, 2013),pp. 2D.6.1–2D.6.9.
[29] T. Grasser, M. Waltl, Y. Wimmer, W. Goes, R. Kosik, G. Rzepa,H. Reisinger, G. Pobegen, A. El-Sayed, A. Shluger, and B.Kaczer, in 2015 IEEE International Electron Devices Meeting(IEDM) (IEEE, New York, 2015), pp. 20.1.1–20.1.4.
[30] T. Grasser, M. Waltl, K. Puschkarsky, B. Stampfer, G. Rzepa,G. Pobegen, H. Reisinger, H. Arimura, and B. Kaczer, in2017 IEEE International Reliability Physics Symposium (IRPS)(IEEE, New York, 2017), pp. 6A–2.1–6A–2.6.
[31] A. T. Krishnan, S. Chakravarthi, P. Nicollian, V. Reddy, and S.Krishnan, Appl. Phys. Lett. 88, 153518 (2006).
[32] B. Tuttle and J. B. Adams, Phys. Rev. B 56, 4565 (1997).[33] B. Tuttle and C. G. Van de Walle, Phys. Rev. B 59, 12884
(1999).[34] B. Tuttle, Phys. Rev. B 60, 2631 (1999).[35] B. Tuttle, Phys. Rev. B 61, 4417 (2000).[36] B. R. Tuttle, D. R. Hughart, R. D. Schrimpf, D. M. Fleetwood,
and S. T. Pantelides, IEEE Trans. Nucl. Sci. 57, 3046 (2010).[37] C. G. Van De Walle, Phys. Rev. B 49, 4579 (1994).[38] C. G. Van De Walle and R. A. Street, Phys. Rev. B 49, 14766
(1994).
195302-10
AB INIT IO TREATMENT OF SILICON-HYDROGEN … PHYSICAL REVIEW B 100, 195302 (2019)
[39] C. Van de Walle and B. Tuttle, IEEE Trans. Electron Devices47, 1779 (2000).
[40] A. A. Bonapasta, Phys. B (Amsterdam, Neth.) 170, 168 (1991).[41] N. M. Johnson, C. Herring, and C. G. Van de Walle, Phys. Rev.
Lett. 73, 130 (1994).[42] N. H. Nickel, G. B. Anderson, N. M. Johnson, and J. Walker,
Phys. Rev. B 62, 8012 (2000).[43] K. Hess, Phys. B (Amsterdam, Neth.) 272, 527 (1999).[44] B. Tuttle, K. Hess, and L. Register, Superlattices Microstruct.
27, 441 (2000).[45] B. R. Tuttle, W. McMahon, and K. Hess, Superlattices
Microstruct. 27, 229 (2000).[46] J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T.
Chassaing, and J. Hutter, Comput. Phys. Commun. 167, 103(2005).
[47] J. VandeVondele and J. Hutter, J. Chem. Phys. 127, 114105(2007).
[48] S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B 54, 1703(1996).
[49] M. Guidon, J. Hutter, and J. VandeVondele, J. Chem. TheoryComput. 5, 3010 (2009).
[50] M. Guidon, J. Hutter, and J. VandeVondele, J. Chem. TheoryComput. 6, 2348 (2010).
[51] C. G. Broyden, J. Appl. Math. 6, 76 (1970).[52] R. Fletcher, Comput. J. 13, 317 (1970).[53] D. Goldfarb, Math. Comput. 24, 23 (1970).[54] D. F. Shanno, Math. Comput. 24, 647 (1970).[55] R. Elber and M. Karplus, Chem. Phys. Lett. 139, 375 (1987).[56] G. Henkelman, B. P. Uberuaga, and H. Jónsson, J. Chem. Phys.
113, 9901 (2000).[57] S. Ling, A. M. El-Sayed, F. Lopez-Gejo, M. B. Watkins, V. V.
Afanas’Ev, and A. L. Shluger, Microelectron. Eng. 109, 310(2013).
[58] L. Gerrer, S. Ling, S. M. Amoroso, P. Asenov, A. L. Shluger,and A. Asenov, J. Comput. Electron. 12, 638 (2013).
[59] U. Khalilov, E. C. Neyts, G. Pourtois, and A. C. T. van Duin,J. Phys. Chem. C 115, 24839 (2011).
[60] U. Khalilov, G. Pourtois, S. Huygh, A. C. T. van Duin, E. C.Neyts, and A. Bogaerts, J. Phys. Chem. C 117, 9819 (2013).
[61] M. H. Evans, M. Caussanel, R. D. Schrimpf, and S. T.Pantelides, J. Comput. Electron. 6, 85 (2007).
[62] R. Buczko, S. J. Pennycook, and S. T. Pantelides, Phys. Rev.Lett. 84, 943 (2000).
[63] E. Kobeda and E. A. Irene, J. Vac. Sci. Technol., B:Microelectron. Process. Phenom. 5, 15 (1987).
[64] E. P. EerNisse, Appl. Phys. Lett. 35, 8 (1979).[65] H. W. Conru, J. Appl. Phys. 47, 2079 (1976).[66] R. J. Jaccodine and W. A. Schlegel, J. Appl. Phys. 37, 2429
(1966).[67] S. C. H. Lin and I. Pugacz-Muraszkiewicz, J. Appl. Phys. 43,
119 (1972).
[68] Y. Sugita, S. Watanabe, N. Awaji, and S. Komiya, Appl. Surf.Sci. 100-101, 268 (1996).
[69] S. Miyazaki, H. Nishimura, M. Fukuda, L. Ley, and J. Ristein,Appl. Surf. Sci. 113-114, 585 (1997), Proceedings of the EighthInternational Conference on Solid Films and Surfaces.
[70] K. Hirose, H. Nohira, T. Koike, K. Sakano, and T. Hattori,Phys. Rev. B 59, 5617 (1999).
[71] A. C. Diebold, D. Venables, Y. Chabal, D. Muller, M. Weldon,and E. Garfunkel, Mater. Sci. Semicond. Process. 2, 103 (1999).
[72] N. Miyata, H. Watanabe, and M. Ichikawa, Phys. Rev. B 58,13670 (1998).
[73] D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. Evans-Lutterodt, and G. Timp, Nature (London) 399, 758 (1999).
[74] D. A. Muller and G. D. Wilk, Appl. Phys. Lett. 79, 4195 (2001).[75] Y. Yamashita, S. Yamamoto, K. Mukai, J. Yoshinobu, Y.
Harada, T. Tokushima, T. Takeuchi, Y. Takata, S. Shin, K.Akagi, and S. Tsuneyuki, Phys. Rev. B 73, 045336 (2006).
[76] C. Kaneta, T. Yamasaki, T. Uchiyama, T. Uda, and K. Terakura,Microelectron. Eng. 48, 117 (1999), Insulating Films on Semi-conductors.
[77] J. H. Oh, H. W. Yeom, Y. Hagimoto, K. Ono, M. Oshima, N.Hirashita, M. Nywa, A. Toriumi, and A. Kakizaki, Phys. Rev. B63, 205310 (2001).
[78] J. C. Fogarty, H. M. Aktulga, A. Y. Grama, A. C. T. van Duin,and S. A. Pandit, J. Chem. Phys. 132, 174704 (2010).
[79] H. Aktulga, J. Fogarty, S. Pandit, and A. Grama, ParallelComput. 38, 245 (2012).
[80] See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.100.195302 for a detailed geometrical anal-ysis of the utilized interface models, including the atomisticmodels as XYZ files, and a discussion of the different typesof defects.
[81] Y. Yu, B. Wang, M. Wang, G. Sant, and M. Bauchy, J. Non-Cryst. Solids 443, 148 (2016).
[82] G. A. Tribello, M. Bonomi, D. Branduardi, C. Camilloni, andG. Bussi, Comput. Phys. Commun. 185, 604 (2014).
[83] A. Stesmans, Phys. Rev. B 61, 8393 (2000).[84] A. Stesmans and V. V. Afanas’ev, J. Appl. Phys. 83, 2449
(1998).[85] G. Henkelman, A. Arnaldsson, and H. Jónsson, Comput. Mater.
Sci. 36, 354 (2006).[86] S. Hashmi and S. Al-Salam, Int. J. Clin. Exp. Pathol. 8, 8786
(2015).[87] W. Tang, E. Sanville, and G. Henkelman, J. Phys.: Condens.
Matter 21, 084204 (2009).[88] M. Yu and D. R. Trinkle, J. Chem. Phys. 134, 064111 (2011).[89] C. G. Van de Walle, P. J. H. Denteneer, Y. Bar-Yam, and S. T.
Pantelides, Phys. Rev. B 39, 10791 (1989).[90] C. G. Van de Walle and R. A. Street, Phys. Rev. B 51, 10615
(1995).[91] C. G. V. de Walle, J. Non-Cryst. Solids 227-230, 111 (1998).
195302-11
